The Art of Mathematical Thinking: Exploring the Mind of a Mathematician
The question of how mathematicians think is closely related to the question, “How does a musician compose?” Similarly, this question is asked to learn how the creative process works. Those who are interested in computer science or especially artificial intelligence can give the correct answer to this question. A real mathematician is not interested in finding the answer to this question, he’s just busy doing math.
Unfortunately, there is no clear way to answer the question of how a mathematician thinks. But we can approach this question as follows; if you watched any chess tournament, the game’s analysis is shared in detail at the end of the match. When you examine the analysis, you will see a breaking point in each game. Similarly, mathematicians also experience a breaking point while working on a problem before finding a solution.
Therefore, it is helpful to analyze a few mathematical proofs to answer our question and pinpoint the breaking points. For example, as we all know, Euclid’s theorem states that there are infinitely many prime numbers.
The proof of this theorem is more beautiful than the theorem itself.
So how did Euclid realize that prime numbers are infinite? Euclid’s approach to the…
